{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Further Hypothesis Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──\n",
      "✔ ggplot2 3.3.0     ✔ purrr   0.3.4\n",
      "✔ tibble  3.0.1     ✔ dplyr   0.8.5\n",
      "✔ tidyr   1.1.0     ✔ stringr 1.4.0\n",
      "✔ readr   1.3.1     ✔ forcats 0.4.0\n",
      "── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "✖ dplyr::filter() masks stats::filter()\n",
      "✖ dplyr::lag()    masks stats::lag()\n"
     ]
    }
   ],
   "source": [
    "# Select this cell and type Ctrl-Enter to execute the code below.\n",
    "\n",
    "library(tidyverse)\n",
    "\n",
    "set_plot_dimensions <- function(width_choice, height_choice) {\n",
    "    options(repr.plot.width=width_choice, repr.plot.height=height_choice)\n",
    "}\n",
    "\n",
    "cbPal <- c(\"#E69F00\", \"#56B4E9\", \"#009E73\", \"#F0E442\", \"#CC79A7\", \"#0072B2\", \"#D55E00\")\n",
    "\n",
    "set_plot_dimensions(5, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "also installing the dependencies ‘tidyselect’, ‘vctrs’, ‘dbplyr’, ‘ggplot2’, ‘haven’, ‘modelr’, ‘tidyr’\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# You should see \"Attaching packages\" and some ticks by the packages loaded.\n",
    "# The \"Conflicts\" aren't a problem.\n",
    "\n",
    "# Other problems loading the library? Try running this cell.\n",
    "\n",
    "install.packages('tidyverse')\n",
    "\n",
    "library(tidyverse)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8 - Goodness of fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Your colleague Althea is not a fan of Prof. Xu's temperature scheme. She has her own ideas about how the star classification should be revised.\n",
    "\n",
    "According to Althea's new theory of stellar evolution, there are two subtypes of hypergiant star, with very different temperature distributions. \n",
    "\n",
    "She says that our galaxy has approximately equal numbers of each subtype. \n",
    "\n",
    "If this theory is true, hypergiant temperatures should be distributed according to:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "P(3000K \\leq \\text{T} \\lt 4000K) = 0.5 \\\\\n",
    "P(4000K \\leq \\text{T} \\lt 40000K) = 0.5\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with uniform temperature distributions within each of the two subtypes.\n",
    "\n",
    "Althea asks you to check whether her theory agrees with your data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question: do hypergiants in the observed data set fit Althea's theory?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pdf associated with the theory is piecewise uniform. We will start by constructing it as a bespoke function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "althea_pdf_single <- function(x){\n",
    "    if(x<3000) return(0)\n",
    "    else if(x<4000) return(0.5/(4000-3000))\n",
    "    else if(x<40000) return(0.5/(40000-4000))\n",
    "    else return(0)\n",
    "}\n",
    "\n",
    "# We can use the Vectorize() function to make a vector-friendly version of this pdf:\n",
    "althea_pdf <- Vectorize(althea_pdf_single)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAHgCAYAAABq5QSEAAAEGWlDQ1BrQ0dDb2xvclNwYWNl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\nBAgQIECAAAECBAgQIECAwNwJ/P8Vk+2K/xmEtQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "x <- seq(0,50000)\n",
    "y <- althea_pdf(x)\n",
    "\n",
    "xlab <- 'temperature'\n",
    "ylab <- 'probability density'    \n",
    "\n",
    "plot(x, y, type='l', col='orange', xlab=xlab, ylab=ylab, main='')\n",
    "legend('topright', legend='theoretical pdf', \n",
    "       col='orange', lty=1, cex=0.8, y.intersp=2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At first glance, the histogram for the hypergiants (type 5) does appear to have a similar shape to this pdf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAHgCAYAAABq5QSEAAAEGWlDQ1BrQ0dDb2xvclNwYWNl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\nBHaewP8FCC2CZfsMM+0AAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "observed <- filter(data, type == 5)$temperature\n",
    "n <- length(observed)\n",
    "\n",
    "xlab <- 'temperature'\n",
    "ylab <- 'freq'\n",
    "\n",
    "bins <- seq(0, 50000, 500)\n",
    "\n",
    "hist(observed, breaks=bins, xlab=xlab, ylab=ylab, col=cbPal[6], main='')\n",
    "legend('topright', legend='observed data', fill=cbPal[6], cex=0.8, y.intersp=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see more clealy, we can overlay a random sample of the same size ($n$=40), drawn from the theoretical distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAHgCAYAAABq5QSEAAAEGWlDQ1BrQ0dDb2xvclNwYWNl\nR2VuZXJpY1JHQgAAOI2NVV1oHFUUPrtzZyMkzlNsNIV0qD8NJQ2TVjShtLp/3d02bpZJNtoi\n6GT27s6Yyc44M7v9oU9FUHwx6psUxL+3gCAo9Q/bPrQvlQol2tQgKD60+INQ6Ium65k7M5lp\nurHeZe58853vnnvuuWfvBei5qliWkRQBFpquLRcy4nOHj4g9K5CEh6AXBqFXUR0rXalMAjZP\nC3e1W99Dwntf2dXd/p+tt0YdFSBxH2Kz5qgLiI8B8KdVy3YBevqRHz/qWh72Yui3MUDEL3q4\n4WPXw3M+fo1pZuQs4tOIBVVTaoiXEI/MxfhGDPsxsNZfoE1q66ro5aJim3XdoLFw72H+n23B\naIXzbcOnz5mfPoTvYVz7KzUl5+FRxEuqkp9G/Ajia219thzg25abkRE/BpDc3pqvphHvRFys\n2weqvp+krbWKIX7nhDbzLOItiM8358pTwdirqpPFnMF2xLc1WvLyOwTAibpbmvHHcvttU57y\n5+XqNZrLe3lE/Pq8eUj2fXKfOe3pfOjzhJYtB/yll5SDFcSDiH+hRkH25+L+sdxKEAMZahrl\nSX8ukqMOWy/jXW2m6M9LDBc31B9LFuv6gVKg/0Szi3KAr1kGq1GMjU/aLbnq6/lRxc4XfJ98\nhTargX++DbMJBSiYMIe9Ck1YAxFkKEAG3xbYaKmDDgYyFK0UGYpfoWYXG+fAPPI6tJnNwb7C\nlP7IyF+D+bjOtCpkhz6CFrIa/I6sFtNl8auFXGMTP34sNwI/JhkgEtmDz14ySfaRcTIBInmK\nPE32kxyyE2Tv+thKbEVePDfW/byMM1Kmm0XdObS7oGD/MypMXFPXrCwOtoYjyyn7BV29/MZf\nsVzpLDdRtuIZnbpXzvlf+ev8MvYr/Gqk4H/kV/G3csdazLuyTMPsbFhzd1UabQbjFvDRmcWJ\nxR3zcfHkVw9GfpbJmeev9F08WW8uDkaslwX6avlWGU6NRKz0g/SHtCy9J30o/ca9zX3Kfc19\nzn3BXQKRO8ud477hLnAfc1/G9mrzGlrfexZ5GLdn6ZZrrEohI2wVHhZywjbhUWEy8icMCGNC\nUdiBlq3r+xafL549HQ5jH+an+1y+LlYBifuxAvRN/lVVVOlwlCkdVm9NOL5BE4wkQ2SMlDZU\n97hX86EilU/lUmkQUztTE6mx1EEPh7OmdqBtAvv8HdWpbrJS6tJj3n0CWdM6busNzRV3S9KT\nYhqvNiqWmuroiKgYhshMjmhTh9ptWhsF7970j/SbMrsPE1suR5z7DMC+P/Hs+y7ijrQAlhyA\ngccjbhjPygfeBTjzhNqy28EdkUh8C+DU9+z2v/oyeH791OncxHOs5y2AtTc7nb/f73TWPkD/\nqwBnjX8BoJ98VQNcC+8AAEAASURBVHgB7d0HnCNnfT9+7XXbd+4VV2xMtzHNtADGBBxq6B1C\n6AkBQgkECAQIJBBaCBBqwBAMCT9CDcV0DNihd7ANuOCKcTuffXe+tv/P16fJX9Zq96S73buV\n9H5er89qNDOaeZ73zGr11Wh3Wy2NAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAwDgLTIzz4I2dAAECBAgQ\nIDCPBZ6Wvt12HvdP1wgQGB+BUzLUk0ZhuItGYRDGQIAAAQIECBAYQYH7ZkznJn8zgmMzJAIE\nhkdgSbr6xkQBPDzHTE8JECBAgAABAkMpsCm9XjeUPddpAgQIzEOBBfOwT7pEgAABAgQIECBA\ngAABAgRmXUABPOukNkiAAAECBAgQIECAAAEC81FAATwfj4o+ESBAgAABAgQIECBAgMCsCyiA\nZ53UBgkQIECAAAECBAgQIEBgPgoogOfjUdEnAgQIECBAgACBuRaov7L9qFnYycOzjX9L/nkW\ntjVbm1jWsaFnZfr2Hffn62Rnn++dTj5+Fjt6RLb1gmSXWdxms6nnZeJWzZ3c7p7UvPcmj0y0\neSagAJ5nB0R3CBAgQIAAAQIEtovAY7KXZ27jnh6Rx380uU0yF8XVoN2baPens7B/deYdN+iG\ntvP6T8r+Ptixz4dl+q877m/r5C2zgdcnK7Z1Qz0eX9u9U8f892S6zPdPFnfMNzlPBPwf4Hly\nIHRj1gTuky3N9G7bmix/frJ61vZoQwQIECBAYP4K7J2uHbAV3bsijzl/Kx43bg+5SwZ8UXLH\neTLwem1fV6Q/N0/60283HpAV63/NNu3vM9F5RbiZPwy3dU5UEfycYejsOPZRATyOR320x/zg\n1qKd7juxYt/fTBnmpo2LJleeXx8Bekty+pTlZhAgQIAAgRETWDjR+uTGyVa9IB+0XZ0HzNbV\nsntkW/UR0cuS7yRnJp2trpTVFbQbJlVMfis5L2naCZn4cVJXWI9PLk2+kqxKbpIcl/ww+V7S\ntKMzUa9zz03q8XVl9OSkHjtTOywL75bUvqqvtd3p2nFZcNOk+nH/5KfJ2uS2ySlJvSF/dnt6\nY253TaovByZl8OWk+R/P+2S6XqN8Prlzckzyo+S0pPp+9+TI5DPJRUmvtjAz62Pd1cr7j5Ky\nbFr53jOpiwFfTy5IOtvy3CnfWu/XSWf/cve6duN8vWtSVzbL+wdJ0/bNxHRjn2nbx+ZxdQ7U\n8SrHOrb1xs1uSfk1rQriOyZlXutUHzvbls6jznW7p8v/Dkn5l9GNkq8nv0y6W/ncK7kw+WLH\nwjq+de5Uv+t7p8ZS59z6RJtHAnWiaQRGSmBil73OWn7/V5/YPagNl56zYs3nX1Y/XDQCBAgQ\nIDAWAhOt1k5/cvOJz7zhwYu+2u+A3/+dTTd545c3Prnf9WdYL7u/7uPBVQh8P6ki44jkOcm/\nJdUenvx7cmVSxU4VIZuSByZVgFWrjxh/InloUuvcMvlu8q7kncmvkpsnVRzWOtWenRyd1D5/\nk1Tx+MHkQUmt16s9IzP/Jam+nJ68Oam+PTPp1Z6VmfXR552Sv0/+Kbk2+XjS9GVNpqswu0VS\nY9gr+XFyu+RnSfXnrKS286nkP5IHJPUGxGHJy5N6bBXOlyTvSJ6QnJR0t6WZUetXq+3umTQF\ncB2DlyVlUVbVzyp2mwK2rKp/ByXfTmqfFyQPTM5Pqr0keVVyWbIqqWP5/uQpyaakXmP1Gvth\nmT/Tth+X5VXU1vlSjtWnZyW3bSc3rYOTU5OyrGNfFzNOSe6dTCb9nEdZbdpW/p9JPpbU+fWH\n5O3JB5InJk17aSZenVTxXQX/T5Lqd7X9kup/HYd7JUcl1UcFcBDmU1swnzqjLwQIECBAgAAB\nArMrsGxRa93NDli4ut/sttPE2lnqQRVaD0v+JLlrUkVOFZRV3FTRsCR5a1JF0yHJ3ZO68lfF\n1TOTzvaA3KkirfKI5A7JPyY3So5J/jypdXZPmlYF2b8kVYwcmbw7+VByg6S7VV+rL29Kqtg6\nLrlH8hfJI5Ne7aGZ+cnkF0ntq8ZRrca1LKkCtIqpDUnt96fJ4UmtW8XR8uS9SdMWZaIKvEqt\n91/Jq5IqLqvPN0k+kzwm6dVWZ+Yd2wtemds/61ip+nFsUoVeM/6/bC9fkNsTk8uTKoCPT26c\nVH/Kr1odm1cnL0sOTWr5E5Jyf3rStO6xVyF/YjLTtp+d5V9Pvp2UzUVJd/tsZvw2KZe7JOVX\nfXp0UvusY1f+WzqPssqMba8sPTq5W1LnbRnWGKvV/v4hqXOizuVyOCeZSKpVUVz9vyapAr2m\nr0q0eSZQJ7ZGgAABAgQIECAwogKXr26t+MSPNlRR1Vc7+9JNVbjNRlvZ3siTcntFUgXgM9rz\n6mZjco/k4rrTbgtz+4ukCuHOVoXm2e0ZX2rffjq357WnT8vt4qQKwC+059X2P9ierqtw70lq\n/1Xc/GfS2Z6YO3VV9HVJrVuttlmpQq+K0UHav2blGnPluKQKt4ckTX9/numPJi9KDk6aVo+r\nflf7clLF9/uSNUm16s9Lr5sa7EsVh6e3H3J5br+U3KR9/7a5vXVShXVd+axWx672++Zkl6T6\n8evkn5Km/UcmXpFUkfiOpGmdY68icEvbroJxplY+VfDeM2n8zsz0cUmdO+XV73mUVWdsJ2Vp\nc/xPzvRZSb2x8v7kvskZyTuTamX0gqTOD22IBMa9AK53buqb/5KkTujmySWTGgECBAgQIEBg\nuAVSGaw85TeT9z7lNxvuPchIcknrislBHtB73fMz+1nJPydVJFyY1BXM1ye/TapwqWLsOcmd\nkpsmByTrkp8mne3cjjt1VbHa9zffXPe1eQ23sGPedzNdBWjTfpSJ2t/RSXcBfGTm7ZQ0BVYm\nr2vL8vXs9vQgN1U4Na3GVZxNAdrM/2wmXpTcqJmR23M6ppvC8Hsd89Zmemtev3ePoQrdI9rb\nrbFXe3fyruumNn9pLGu9GsOvOpY1kzWGKpw7W+fY+9l297Hu3FZN36o9o4reznZqx51+z6OO\nh/ScPLlrbr0Jcc/2vDpvftO1vBwv65rn7jwX2JpvoHk+pOt17+m5d/fkyUnzxFgr1LtI70tu\nV3fard7FqXe13pDUE7JGgAABAgQIEBhqgcnJ665a7TboIFKtNcXXoA/tXv9tmfGB5F7JCclD\nk0cmN0mq0D0t2ZTUldoqlL/Tnt4/t52t83VcM78eN1PrHkMVodUu3Xxzva/VlwuSh11v7uY7\ntWzQVoVq02o67ylc97uh1zYzc7uhPX1Rbg9tT3c+rj3ruuK5md7a2+aqZq/HN+N7RhbWVd7u\nVgVt+dcbBN2tXjNX/ztb5xj62XbnY3tNN6/L682IzlamdUx3T/o9jzof32u6eXOlWVbbb86X\nqhX2bha0b3fJ7Yquee7Oc4FRL4DvEP9HJ3+RNE+cB2f6m0n9MKh3Dn+Q7JrcLXltsl/yvEQj\nQIAAAQIECAy7QBUjnQXJ9hxPfbT2mclfJx9v58Tc1pW7OyVLkhsmdYWvuQpYRc0tkiuTbW11\nxa6Kpmb8N830nkm99utuv8iM+t3iWrfpS63zT0ld9ftx3dnK9sv24+6a27pi2rR67Vm/t3tm\n0hTAzbKtva2CrdqCzTd9fa2xVyufk66b2vyl3qyoPr8oqTE8MamCr/ONhT/K/R8l07V+tl2P\nrX5P1+fT2xu/fW47r8B+K/d/knwtma3z6Nhs64tJ0+6ciaobqlXd8LfJzkkdt2r3SOo81oZI\nYLoTbYiGMHBXq8it4vdZSX0jPSN5THLj5MPJc5M/TjQCBAgQIECAAIGtF6iriQ9I3pgclhyQ\nPCqpK3r18eQqROsq7oOSZUktf2dSr8mqyNjWtm82UK/tbpbcO/lIckpyatLd3pEZVXT/W1Kv\nA/dKXpa8MPllsi2txvrlpLb9pGTfpLb74uRdSRnMVtuQDV2bHJfUGwv9tF9lpU8m9Zq4sntS\nV+z/PWm295ZM1xXgTyR/lJTpB5Ojkvcl07V+tl2PraL6pkkV3LWfznZ27nwseV3yhKSOzbOT\nOyT/mszmefT2bK/Ox8OT9yeHJjWvWp1LZVt9qTdX7p68ItGGTGDBkPV3Nrpb7+TUE1F9JKez\nrc6dpySXJcd3LjBNgAABAgQIECAwsMBVecTTkiqWqhi+MHlIcv+kPjZ7VvKKpNapj5eek9RH\ndZ+f3DjZI9mWVlcOFya/SP4nuTh5cFL76G5/yIwqfOsK55eSul+F0DOT05JtbY/OBur153uS\n3yc1xir263a2WxXztb8aR7/tz7Pi55K3JlckH0g+mrw8qXZ+ckJycFJXRMv0Nkkdz68nM7Ut\nbbseW/vbMzklOTbpbnWOfDupYvvS5J+SFyR1jGfzPKrz5CPJb5Pqx0OTXybVLkwekOyX/Dip\nNzVOTmq+NkQCE0PU163pan2T1DddvZNVT6zVqsCtd6+q2O3VvpWZlycP7LXQvHkv8O6J3Q46\nevkD/6mO/fVa+/8AvyEz6wdxPWFqBAgQIEBgPgt8Mp2rq1/Pnc+d7LNvu2a9Ki4v6rF+vR49\nLKkiq1dxmtkDt/fmEXUF9PbJ3klduVuV9NOq8F6aVME8222nbHD/pI7rXLbaT13oumbAnSzJ\n+gcm5ySTSa+2T3tmvUkwSNvStus8KPt6HT5dq3FV/36XrOtaaVvOoxOyrS8kN0zqHK1zpn4n\nfLpWRXCdT6unW2HE5texqzdHnj4K41o0CoMYcAz1MYmjpnnMXplfT5QnTrPcbAIECBAgQIAA\ngcEFrspDKr1aFVpzWRDWFcNBWl0Bnau2Jhuey7E2/a79bE2ronJL/Ru08G36saVt13kwU/Fb\n26lx/aYmerR6/Jb63uNhU2bVmyUzFb/1gN9PeZQZQyNQ7wyNQ6uPnJyUPC85Nbld0n2F95DM\ne1tS73B8I9EIECBAgAABAgQIECBAYIQERv0K8OdyrOrjz8ckj2knN9e1KnY/3Z6+X27rY0bl\nUQXyRxKNAAECBAgQIEBgOAVekW4vG86u6/UOEPh29nl0sqUrvzuga3Y52wKjXgB/LGCVarsl\nVQg3qd8TaFr9gYT6SEUVvvV7NvURCo0AAQIECBAgQGDuBZ6dXdQFiO/P4q7On8Vtbc2m7p8H\n7ZzUH5Lqtx2ZFf80qYs0a/t9UNarQn+Q9QfY9NisenVG+rOxGe2YD3TUC+DOw7syd+qjzb0+\n3lx/Ja9+/3e2/vDCntnWa5P6OHU/rdY7PLljPytbhwABAgQIECAwQgKvyVhekcxmAbyjeR6b\nDuybDFIA19+oeX3y/qTfgvZJWfdPkkckGgECfQiMUwE8E8fW/qGAmbY5yLK6On2HpArh7r9o\nN8h2rEuAAAECBAgQ6BSoq5C7d87oc7quiE33R6v63ITVtoPAA7KPfi+4bIfu2AWB+S+gAJ6b\nY1R/we5pA2z6Tln3vgOsb1UCBAgQIECAQB8CE/l7KJN372PF7lWuzIz6lzSz0XbNRk5I6t/X\nnJnU/0/t9Yb/zTP/HsmF7XVW5baz1bJbJZcl30lqW51tee4cn9ww+XXSuZ+6Gnvb5JTkkUn9\nteD6a7+bkv9NOtvtcmdxclp75kzbbR63IhP3SmqsJzczt3C7IMvrAsitkxpPr1bF7d2SmyRl\n9tOkWffYTO+f1Ov5+sj1V5Lmok45VeoY1v+0LYt+rypnVY3A6AoogEf32BoZAQIECBAgMO4C\nExMrFu53s5MX3/SEb/VLsfGCHx2x/tdfr4/wzkarN/k/kdSvmv04qeLyZ8mDkrOSpj0sEy9J\natldknOTujhQRe5E8tGkirzvJ/V/aI9InpP8W1Lt6KT2c1Dy7eQWyQXJA5Pzk/o3lx9PPpM8\nNKlC8c3JM5MqIpvisP4uzP8k706qAN7SdrPKdQVs+W5Mqnh/Q3JRckkyXVuaBVWMV79+lLw1\n+WbS2Q7LnfqDrXX7w+RmSRXy/5I8N3lcctOkfP4++UFS43pv8sTkJ0kV8kclZyRlf3WiERhr\nAQXwWB9+gydAgAABAgRGXmDJzlcvPvg2MxVj1yPYePl5e11vxtbf2TkP/VBSVy2fnJyX3DKp\noq6KtLpa27RbZaIKtbpaeXhS67wluU9y86QK5OOSbyTV3pk8K3lHUgXgicnlyR2TPyS7JVVQ\nVrFYj61WV1OXJXsmdWW0CtYXJ1VYfyypdu+kiswTkwXt25m2W4XsJ5K66ltjvDJ5TFLj/loy\nXavf9T04OSYpnyrYP5l0tupb9aWunK9Kqj//nvxVUm8WPDupbdS47pdU++Ok+lFj+mxSrZb9\nT/LA5MOJRmCsBUa9AH5qju6uW3GET81j6l0/jQABAgQIECAw3AIb1i3dcNm5y/sexLqrq3Cd\njXZsNlLF7EOSKn6r/Tz5aPKipIq3Zn4Vi79NqtWV4TclVexVIbsyqfak5IqkCsZnJE27XSZu\nnVTh+Yf2zHrM+5I3J7u059XNvya1jUq1ryR1JbUpgB+f6VOS6kNdnd3Sduuq7KHJA5Jmmydl\n+inJTK0K1HoToMZS7RdJ9fXtdafdXpXb1yVV/FZbkNR69fp9t6Su9na372RG9fnHHQvOzPSm\nZLbe2OjYtEkCwycw6gXwX+aQ1Dtrg7ZX5AEK4EHVrE+AAAECBAjML4HJydUbL/zp/dckA3as\nKboGfNj1Vq+P504mp19v7uYrk1UA3yhpCuAvdK1Tv8Nb7Yjkh0ld7f3n5AnJhclnktcnVTQf\nmVR7d/Ku66Y2f1nYnq5tNK0K2872/typ7JmsTx6U1OvHav1s9+jNq173O8ftyetuasw36ZzR\nMb0i0zdMmjE2i7qdfp8FVZy/Nrl5Ul7XJtWasW2+9/9/reNWV6XL4aikjkGtW8XzdI/JIo3A\n+AiMegF8nxzKjyd3Sj6VvC/pp53Rz0rWIUCAAAECBAjMb4HJP03/9t+KPl65FY/pfsjazKiP\nJ1dB1hRutc6G+pJ20eab6752X82sYq9a04+3ZfoDyb2SE5KHJo9MbpKsS6rVVeHuorLmV9F7\ncE2kVZ86W71O/Lfk4Un1cWPy/5Jq/Wy36edOWb9z2zOZ13q1r52Tztb9mOpXFfx1pfi/k28n\nd01m+hjzn2R5fdz5S8lJybeSel27OqljoREYe4FRL4AvzhG+R/KNpIrhVyY/SjQCBAgQIECA\nwDgIXJ5BVnZE+2V7p1W0fbajA3fLdBVk9dHcpt2mmWjfViFXVzPPTW6bPDP566QK1sqJSf3K\n2p2S+lhwtZsmVfQ1rYrk2nddbZ6uVTH6keRhSVP8XtNeuZ/tfr+97l1yW4VntcXJPZNmWc3r\nbOtz5yfJnZN3dSyowr5pSzLxZ0ld9X5ZMzO3dVW3WnM1t66w19Xdpj0pE79J6nVv047JxETS\nPKaZ75bAWAp0fsOMKkC9w/bk9uDeOqqDNC4CBAgQIECAwDwT+G768+WkrmRWYbZv8sLkxUkV\nfpuSpj0lE49J6kpqfVz7fsnrkipK66ruA5I3JoclBySPSmpZ7eNXySeTZ7Sze27vlfx7Uleb\n67XgTK0+An1ccnxS003rZ7u/y8p1xbiuUNcV6UOTtycrkplajeXRSV2cqSu/1fe6Wt+0uvpc\nvx98XFLL62px+TwvqVb3q1WxXoX/XZOy+15yw+QOyYKkit/minEt1wiMvUB9Y4xDq3fwXpLs\nmhw1DgM2RgIECBAgQIDAPBCoIq+K1Pckv0+en7yzfZub/2uvz9Rrkiro6gpvFc1VAFe7Knla\ncrOkiuELk4ckVShflFT78+RzSV3suCL5QPLR5OXJllr174zk3OSbXSv3s90/y2NqG1U8n5Pc\nPPmPZDKZrlXfXpBU4V9jeHXSjDeT17W/zdelyQVJjekvkxOSKvyrwK1W49wzOSU5NqmPS5fD\n15LVyeeT2u4Xk+YxmdQIjK/AxPgOfV6N/E7pzalJPcnVO37a1gu8e2K3g45e/sB/el/3JjZc\nes6KNZ9/2Rsyv36Ant693H0CBAgQIDDPBOqq5tnJc+dZv7amOzvlQXUls8YzUzs0Cy9Orp1m\npbqYsUtSRWOvtiQzD0zOSSaT2Wr9bLfGuFtS/e+31WvxQ5Lzks4r4p2PL7cqZuuNgF6ttrFH\ncnnHwp0zXYXx+R3zTBLYWoE6/+vNpadv7Qbm0+MWzafO6AsBAgQIECBAgMBICqzJqLZU/NbA\nz93C6KsInK4QrIfWhYR+9lPrDtL62W6NsTJIqyJ9S2PeUkFd2+gsfmv/VTBXNAIEugTG5SPQ\nXcN2lwABAgQIECBAgAABAgTGTUABPG5H3HgJECBAgAABAgQIECAwpgI+Aj2mB96wCRAgQIAA\ngaEQqNdq9fucGgECBHaUQP0O8Mg0BfDIHEoDIUCAAAECBEZMoH7v9K/aGbGhGQ4BAkMm8O4h\n6++03VUAT0tjAQECBAgQIEBghwrUv72p/16gESBAYEcLXLijOzBb+1cAz5ak7RAgQIAAAQIE\nZlfg0myuohEgQIDALAn4I1izBGkzBAgQIECAAAECBAgQIDC/BRTA8/v46B0BAgQIECBAgAAB\nAgQIzJKAAniWIG2GAAECBAgQIECAAAECBOa3gAJ4fh8fvSNAgAABAgQIECBAgACBWRJQAM8S\npM0QIECAAAECBAgQIECAwPwWUADP7+OjdwQIECBAgAABAgQIECAwSwIK4FmCtBkCBAgQIECA\nAAECBAgQmN8CCuD5fXz0jgABAgQIECBAgAABAgRmSUABPEuQNkOAAAECBAgQIECAAAEC81tA\nATy/j4/eESBAgAABAgQIECBAgMAsCSiAZwnSZggQIECAAAECBAgQIEBgfgssmt/d0zsCAwsc\nNHnNZYdf/T9/98Qpj9y0oTnfl01ZZgYBAgQIECBAgAABAiMv0BQEIz9QAxwbgcOWL7p298P2\nvGrf7hGvX7dxyRkrr5t7QL7+uHu5+wQIECBAgAABAgQIjLaAAni0j+9Yjm7/3RZe+6LH3fq0\n7sH/7oIrdnvpe390cPd89wkQIECAAAECBAgQGA8BvwM8HsfZKAkQIECAAAECBAgQIDD2Agrg\nsT8FABAgQIAAAQIECBAgQGA8BBTA43GcjZIAAQIECBAgQIAAAQJjL6AAHvtTAAABAgQIECBA\ngAABAgTGQ0ABPB7H2SgJECBAgAABAgQIECAw9gIK4LE/BQAQIECAAAECBAgQIEBgPAQUwONx\nnI2SAAECBAgQIECAAAECYy+gAB77UwAAAQIECBAgQIAAAQIExkNAATwex9koCRAgQIAAAQIE\nCBAgMPYCCuCxPwUAECBAgAABAgQIECBAYDwEFMDjcZyNkgABAgQIECBAgAABAmMvoAAe+1MA\nAAECBAgQIECAAAECBMZDQAE8HsfZKAkQIECAAAECBAgQIDD2AgrgsT8FABAgQIAAAQIECBAg\nQGA8BBTA43GcjZIAAQIECBAgQIAAAQJjL6AAHvtTAAABAgQIECBAgAABAgTGQ0ABPB7H2SgJ\nECBAgAABAgQIECAw9gIK4LE/BQAQIECAAAECBAgQIEBgPAQUwONxnI2SAAECBAgQIECAAAEC\nYy+gAB77UwAAAQIECBAgQIAAAQIExkNAATwex9koCRAgQIAAAQIECBAgMPYCCuCxPwUAECBA\ngAABAgQIECBAYDwEFMDjcZyNkgABAgQIECBAgAABAmMvoAAe+1MAAAECBAgQIECAAAECBMZD\nQAE8HsfZKAkQIECAAAECBAgQIDD2AgrgsT8FABAgQIAAAQIECBAgQGA8BBTA43GcjZIAAQIE\nCBAgQIAAAQJjL6AAHvtTAAABAgQIECBAgAABAgTGQ0ABPB7H2SgJECBAgAABAgQIECAw9gIK\n4LE/BQAQIECAAAECBAgQIEBgPAQUwONxnI2SAAECBAgQIECAAAECYy+gAB77UwAAAQIECBAg\nQIAAAQIExkNg0XgM83qj3CP3dkuWJlcnVybXJBoBAgQIECBAgAABAgQIjLDAuFwBvnWO4XuT\nS5LLk7OT05PzkyqCf5u8K9kn0QgQIECAAAECBAgQIEBgBAXG4Qrwy3PcXtk+dr/L7WlJFcFV\n+NaV4D2TQ5KnJQ9Nnp18ONEIECBAgAABAgQIECBAYIQERr0AfniOVRW/X0hemvww6dUmMvOu\nyRuTk5JzklMTjQABAgQIECBAgAABAgRGRGDUPwL9oByns5K6na74rUM5mZyS3DtZlTwh0QgQ\nIECAAAECBAgQIEBghARGvQA+OseqPvJ8bZ/H7Iqs99PkwD7XtxoBAgQIECBAgAABAgQIDInA\nqBfAF+U43DZZ3OfxqL8QXUVz/YEsjQABAgQIECBAgAABAgRGSGDUC+AP5FjdNPnv5A4zHLfm\nd4Drd4V3Tj45w7oWESBAgAABAgQIECBAgMAQCoz6H8Gqv+a8b/Lq5AHJBcn5yWXJVcmuSf0V\n6EOTA5INyfOTbycaAQIECBAgQIAAAQIECIyQwKgXwPXHrd6cfCp5TXK3pPtK8OrMuzCpvwD9\nluS8RCNAgAABAgQIECBAgACBERMY9QK4OVz1l6Af3b5TV33r//8uSy5JViaz3eqq8muTJX1u\neJ8+17MaAQIECBAgQIAAAQIECGylwLgUwJ089dHnikaAAAECBAgQIECAAAECYyQwjgXw9ji8\nl2cnTxtgR3fKuvcdYH2rEiBAgAABAgQIECBAgMCAAqP+V6AH5LA6AQIECBAgQIAAAQIECIyq\ngAJ4VI+scREgQIAAAQIECBAgQIDA9QRG/SPQT81o649eDdpOzQNOG/RB1idAgAABAgQIECBA\ngACB+Ssw6gXwX4b+mK3gf0UeowDeCjgPIUCAAAECBAgQIECAwHwVGPUC+D6B/3hSf2Sq/hfw\n+5J+2hn9rGQdAgQIECBAgAABAgQIEBgegVEvgC/OobhH8o2kiuFXJj9KNAIECBAgQIAAAQIE\nCBAYM4Fx+CNY1+aYPrl9XN86ZsfXcAkQIECAAAECBAgQIECgLTAOBXAN9RfJS5L6g1hHJRoB\nAgQIECBAgAABAgQIjJnAuBTAdVjfmByd/KzuaAQIECBAgAABAgQIECAwXgLjVACP15E1WgIE\nCBAgQIAAAQIECBC4noAC+Hoc7hAgQIAAAQIECBAgQIDAqAoogEf1yBoXAQIECBAgQIAAAQIE\nCFxPYNB/g/SuPHq/622hvzv/kdX+u79VrUWAAAECBAgQIECAAAECBGZfYNACuP6I1C2T5e2u\nbMztlcmeyUR7Xq+b7/SaaR4BAgQIECBAgAABAgQIENheAoN+BPrx6dg1yaeT2ybLkr3bt/fJ\n7a+SKnbrKvFeHXlzpjUCBAgQIECAAAECBAgQILDDBAa9Avzv6emPkgcnmzp6vS7TX0h+npyR\nPCR5Z6IRIECAAAECBAgQIECAAIF5ITDIFeCl6fEdkw8lncVv50DOz50fJ3fvnGmaAAECBAgQ\nIECAAAECBAjsaIFBCuAN6ezVyYEzdHpxlh2RXDbDOhYRIECAAAECBAgQIECAAIHtLjBIAVx/\n8OpLyUuSY3v0dOfMa/5KdH0cWiNAgAABAgQIECBAgAABAvNGYNDfAf7H9PyPkvpDV6ck9Uev\nViUHJccn+yb1e8L/k2gECBAgQIAAAQIECBAgQGDeCAxaAP80Pb998r7krsndkqb9PhNPT97b\nzHBLgAABAgQIECBAgAABAgTmi8CgBXD1+6Kk/uVRfXz6xkn9y6PfJhckk4lGgAABAgQIECBA\ngAABAgTmncDWFMDNIOovQZ/eTjPPLQECBAgQIECAAAECBAgQmJcCg/wRrO4B7JQZRyV3aC/Y\npXsF9wkQIECAAAECBAgQIECAwHwR2JoC+JB0/qPJNUn9TvAbkmofSl6d1P8L1ggQIECAAAEC\nBAgQIECAwLwSGPQj0Aek9z9M9krqL0DXvz5q2kQmXpo8KLldsjbRCBAgQIAAAQIECBAgQIDA\nvBAY9Arwv6bX9dHn+gvQN0+qGG7aQzPxmuQWyZ81M90SIECAAAECBAgQIECAAIH5IDBoAXzP\ndPrtybd6dH5j5r0yWZncscdyswgQIECAAAECBAgQIECAwA4TGKQA3jW93CM5Y4bers+yX7TX\nm2E1iwgQIECAAAECBAgQIECAwPYVGKQAvipduzi5/QxdrCK5PgJd/x5JI0CAAAECBAgQIECA\nAAEC80ZgkAK4Ov355CnJXyXLk862e+58MNkt+VLnAtMECBAgQIAAAQIECBAgQGBHCwxaAD8v\nHb4weWtyQXLn5PDkk8lvkz9NTky+kmgECBAgQIAAAQIECBAgQGDeCAxaAF+Znt8meVeyLNkv\nuUFShW+1Zyd1hVgjQIAAAQIECBAgQIAAAQLzSmDQ/wNcfwF6TVIfgX5mcmiyf3JOUleGNQIE\nCBAgQIAAAQIECBAgMC8FBrkCvDQjqP/ve/9kQ1L/9uis5NRE8RsEjQABAgQIECBAgAABAgTm\nr8AgBfC6DGNVsnMyMX+HpGcECBAgQIAAAQIECBAgQGCqwCAF8GQe/uD2Jj6d2xOSI5L610fd\nqavFGgECBAgQIECAAAECBAgQmDcCgxTA1ek3JHUFuD4G/YXkN8nKHnlx5mkECBAgQIAAAQIE\nCBAgQGDeCAz6R7BOT8+v6KP3Z/SxjlUIECBAgAABAgQIECBAgMB2E9hSAXzT9OTs5Np2j/yL\no+12aOyIAAECBAgQIECAAAECBGZTYEsfgf5hdvbWjh0+N9PHddw3SYAAAQIECBAgQIAAAQIE\nhkJgpgJ4cUawJNmnYyTPyvTdO+6bJECAAAECBAgQIECAAAECQyEw00eg12cEP07um/xX8vNk\n9+Ruyd8lM7VTsrCiEZhtgXpT5k3J8mk2fMDk5OTCaZaZTYAAAQIECBAgQIDAGAvMVAAXSxW6\nVfw+op3ctI5vp6ana6/MAgXwdDrmb4vAfnnwM2+6b+uHyxZPNL+b/n/b+8XFk8tbk5vqX3Zp\nBAgQIECAAAECBAgQuJ7Algrg+ldHhyT1/37r6u9JycnJfyQztbNmWmgZgW0VeNPDF/33CTdb\ndGn3dvb6m7W3yrz6+L5GgAABAgQIECBAgACB6wlsqQCulev//NYfw6pWt6clX6k7GgECBAgQ\nIECAAAECBAgQGBaBfgrgzrHcr/OOaQIECBAgQIAAAQIECBAgMCwCC4alo/pJgAABAgQIECBA\ngAABAgS2RUABvC16HkuAAAECBAgQIECAAAECQyOgAB6aQ6WjBAgQIECAAAECBAgQILAtAgrg\nbdHzWAIECBAgQIAAAQIECBAYGgEF8NAcKh0lQIAAAQIECBAgQIAAgW0RUABvi57HEiBAgAAB\nAgQIECBAgMDQCCiAh+ZQ6SgBAgQIECBAgAABAgQIbIuAAnhb9DyWAAECBAgQIECAAAECBIZG\nQAE8NIdKRwkQIECAAAECBAgQIEBgWwQUwNui57EECBAgQIAAAQIECBAgMDQCi4ampzpKYLPA\n4rr53M83PfT75264thtlstVa0j3PfQIECBAgQIAAAQIECJSAAth5MGwCe1eHr5lcvv+qiSVr\npnb+0gUpgjUCBAgQIECAAAECBAhMEVAATyExYxgEbnDIwT+/6RH7XTKlr1/+2mGZNzFlvhkE\nCBAgQIAAAQIECIy9gN8BHvtTAAABAgQIECBAgAABAgTGQ0ABPB7H2SgJECBAgAABAgQIECAw\n9gIK4LE/BQAQIECAAAECBAgQIEBgPAQUwONxnI2SAAECBAgQIECAAAECYy+gAB77UwAAAQIE\nCBAgQIAAAQIExkNAATwex9koCRAgQIAAAQIECBAgMPYCCuCxPwUAECBAgAABAgQIECBAYDwE\nFMDjcZyNkgABAgQIECBAgAABAmMvsGjMBQ7N+G+SXJKckaxJNAIECBAgQIAAAQIECBAYQYFR\nvwL89ByzDyc7dR27o3L/e8k5ycnJj5KLkhclCxONAAECBAgQIECAAAECBEZMYNQL4DvkeD06\nWdJx3A7O9DeT2yXfT96VfCS5Onlt8vpEI0CAAAECBAgQIECAAIERExjHj0BXkbtb8qzkbR3H\nc+dMvyd5bvK55MuJRoAAAQIECBAgQIAAAQIjIjCOBfCdc+y+m3QWv3U4VydPSU5Ijk+2pQDe\nM4+vQrvzynPuTtv2mXaJBQQIECBAgAABAgQIECAwKwKj/hHoXki7ZubPei3IvPojWKcnt5xm\nudkECBAgQIAAAQIECBAgMKQC43gF+Ac5VvVHsHq1vTLz9smJvRYOMO/yrPu0Ada/U9a97wDr\nW5UAAQIECBAgQIAAAQIEBhQYlyvA9ZHnk5LnJacm9QewHph0tkNypz4WXR9b/kbnAtMECBAg\nQIAAAQIECBAgMPwCo34FuP6Y1e7JMclj2snNda2K3U+3p++X208m5VEFcv1VaI0AAQIECBAg\nQIAAAQIERkhg1Avgj+VYVarVX36uQrjJRM1st/rfv/X7v1X41l+Bnkw0AgQIECBAgAABAgQI\nEBghgVEvgDsP1crcqY829/p485cyv37/d32iESBAgAABAgQIECBAgMAICoxTATzT4aurvxoB\nAgQIECBAgAABAgQIjLDAuPwRrBE+hIZGgAABAgQIECBAgAABAv0IKID7UbIOAQIECBAgQIAA\nAQIECAy9gAJ46A+hARAgQIAAAQIECBAgQIBAPwIK4H6UrEOAAAECBAgQIECAAAECQy+gAB76\nQ2gABAgQIECAAAECBAgQINCPgAK4HyXrECBAgAABAgQIECBAgMDQCyiAh/4QGgABAgQIECBA\ngAABAgQI9COgAO5HyToECBAgQIAAAQIECBAgMPQCCuChP4QGQIAAAQIECBAgQIAAAQL9CCiA\n+1GyDgECBAgQIECAAAECBAgMvYACeOgPoQEQIECAAAECBAgQIECAQD8CCuB+lKxDgAABAgQI\nECBAgAABAkMvoAAe+kNoAAQIECBAgAABAgQIECDQj4ACuB8l6xAgQIAAAQIECBAgQIDA0Aso\ngIf+EBoAAQIECBAgQIAAAQIECPQjoADuR8k6BAgQIECAAAECBAgQIDD0AgrgoT+EBkCAAAEC\nBAgQIECAAAEC/QgogPtRsg4BAgQIECBAgAABAgQIDL2AAnjoD6EBECBAgAABAgQIECBAgEA/\nAgrgfpSsQ4AAAQIECBAgQIAAAQJDL6AAHvpDaAAECBAgQIAAAQIECBAg0I+AArgfJesQIECA\nAAECBAgQIECAwNALKICH/hAaAAECBAgQIECAAAECBAj0I6AA7kfJOgQIECBAgAABAgQIECAw\n9AIK4KE/hAZAgAABAgQIECBAgAABAv0IKID7UbIOAQIECBAgQIAAAQIECAy9gAJ46A+hARAg\nQIAAAQIECBAgQIBAPwIK4H6UrEOAAAECBAgQIECAAAECQy+gAB76Q2gABAgQIECAAAECBAgQ\nINCPgAK4HyXrECBAgAABAgQIECBAgMDQCyiAh/4QGgABAgQIECBAgAABAgQI9COgAO5HyToE\nCBAgQIAAAQIECBAgMPQCCuChP4QGQIAAAQIECBAgQIAAAQL9CCiA+1GyDgECBAgQIECAAAEC\nBAgMvYACeOgPoQEQIECAAAECBAgQIECAQD8CCuB+lKxDgAABAgQIECBAgAABAkMvoAAe+kNo\nAAQIECBAgAABAgQIECDQj8CiflayDoFRENjU2jTRHsdzc/vIHmM6IPMWJ7/rsaxmrU1ekFxd\nd2ax3S3b+vOk6V/3ptdlxt8ml3cvcJ8AgZEWeFBGV5mu1XPR85J6jtAIdAq8PHcO75zRNf39\n3H9b17y5vnuT7OBFyXQXXzZl2WuTMxONAAECcyagAJ4zWhuebwIbN66v4rbV2nmvwyeWLl/e\n3b/JlRccvcuiDYuO3GdiWfeyDZtaC39+0eSxmf9vyU+7l2/j/fvtvLj1wBvvO3FG93byamDi\npxdM3jHz35+c1r3cfQIERlrg4a3FO99zYvk+Z00Z5cZ1Syevuug2mf+65Lwpy80Ya4GJidbz\nDt6jdfGeO01MeeP04lWT+1+6qnXshsntXgDfeeGC1qOOOmDix70Ozs8umjxm46bWN7NMAdwL\nyDwCBGZNQAE8a5Q2NCwCiw+97WnLbvf4+iF7vbbqo3/xsn2XX73LD1689MTrLcidM36/ceeb\n/8P6KoDnpO27onVer/2uXL1x4Z4vXF8FsEaAwBgKTKzY78zl93vVh7qHvv7Cn+699iuvrwJY\nI9BT4JG3WfjV1z5o8ZRi83Enrjvu//1g0zE9HzTHM5cuaq3s9bOudrvieWtfudpnGeb4CNg8\nAQIlMN3HUOgQIECAAAECBAgQIECAAIGRElAAj9ThNBgCBAgQIECAAAECBAgQmE5AATydjPkE\nCBAgQIAAAQIECBAgMFICCuCROpwGQ4AAAQIECBAgQIAAAQLTCSiAp5MxnwABAgQIECBAgAAB\nAgRGSkABPFKH02AIECBAgAABAgQIECBAYDoBBfB0MuYTIECAAAECBAgQIECAwEgJKIBH6nAa\nDAECBAgQIECAAAECBAhMJ6AAnk7GfAIECBAgQIAAAQIECBAYKQEF8EgdToMhQIAAAQIECBAg\nQIAAgekEFMDTyZhPgAABAgQIECBAgAABAiMloAAeqcNpMAQIECBAgAABAgQIECAwncCi6RaY\nT4DAdhM4aMOm1sGv+cKGJ3bvccPGyYn2vBXdy2bh/h2yjWckzT66N3mrzDgjWdu9oH3/27l9\nzzTLZpr9qCx8VTLdfjdl2eOT7yaDtpfkATee4UE/zrJ/mWb5izL/ZtMsq9k/S944w/K5WHRY\nNvqyZOE0Gy+rNyfVt9lsN8jG6hhN9zPiyCy7PLks6dUuyMyX9lqwjfOekMcfP8M2Ls2yF8yw\nfLpFu2XBPydLp1lhMvM/mHxtmuXDNntJOvymZPkMHf9kllVmsy3Ixmq/u8+w0c9n2X/NsHxr\nF70hD9x7hgd/NcvqGPdqr8vM/XotaM/7Rm7fP83y12T+gdMs2yvz90x+Pc3yo9vL1kyz/H8z\n/53TLNuW2TM9j9b3ygHJ6dPsoJ6Tasy/nWb5XM3+eDZ81DQbX5b5eyQXTbN818z/eXLeNMvP\nyvxXTbPMbAIEhlBguhc3QzgUXSYwtAJHbJqc2HXVxO77do9gw8TGFIlX1OxDu5fNwv17txYs\nftDEbjf4Va9tTV5x7q0mdtlrj9aS5Rd2L59cc8WBrWtX3bw1Obk1BfCjFy9s3ejwfZes6t5u\n3T/zonUrUm08KJNbUQBPPG9ilz0vS5+nFmZrV+47ufaqu7QmN/1Lr/0umGg95wa7ta7ee5eJ\nKqKu1/5w9eQ+F1/VusfGye1eAB+bfj3u6BtM/OB6HWrf+cVFk0ev39T6Ye7OdgF8TLb5xIk9\nDu15DBasPPfYPXZurTpot4kp586Vayd3O+ey1mPz+Je2uzlrNwsnWk/Mfo88aPeJKS9UV62b\nXP7bP1z3ArhevK8bcKdV0D9tYo+Dv9NqLagX8Ndrk1dddOPWxnX1jTgqBXAVc8+c2PWAH7YW\nLrn2eoPNncmr/3B4a/3qxZn8ZPeybbxfxdNzJlbs95PWomWru7c1ufrSQ1vXrk5BODnbBXAV\n/M8/Yp/Wz1Ysmbi6e7/nXzl58BWrW4fk+3u6AviFE8v3/Xlr8U5TnrMmV19xUJ4Lc/5MTlcA\nv/CwvVpn7r5sYuWU/a6cvFn2u2LTbof2fjPwinOPOWiP1t577TxxfvdjL1o1ecBlq1rHbJic\n/QI4zznPy3PhZXkunPI8etZlkzdava611y0PmJjyfVJ9/OmFk7feNNn6Sia3awGc54b77bVi\nwcQeuyya8mbBxVeu32XV2smFR+6/ZMrP2OrzWb9ft2L9gmXH5rzcqe5fr627es/Jay7Pz6NJ\nBfD1YNwhMNwCCuDhPn56PyICEwsWrD/6Nkef1j2c1WvXLWp97luHd8+ftftLdr54+f1ffWKv\n7a36j8ffceGBt/nBTnd4wsndy1d/7c1/svGCHx3UPb/f+7ssndjwd0/7o0/3Wv/P/+Grj80V\n8a1tk4sOvv3Xl93+sVMKxtXffuddN5592h1n2vADbrnglLc9asmUou9pJ62784n/u+keMz12\nrpYtWtBa/YMXLz2x1/b3/Ju1L1k55eVerzW3Zt7E+unOjdUf/rNb3/KAyQu+8pyp/XrNyRtu\n9vLPbJjpKvzWdOb/HnPrgyd+8oW/Wjrl3Hn71zcc/uyPbTjq/1YcbCLvubRay+7xvJMW7bL3\nlILw6k88/xmTV18y2BaHYO2lt3/cfy++wdFT3vC5+rMvf9zk5WfP2QiWHv2QTy0+/M4XdO9g\n9cn/8PCNl0x3MbR77cHvP+fuiz73zOMW1dW867U/edu1D/zqGZM7X29m153FNz7+C0tvcb8p\nnVv9lTfeb+OFP5npynLrSXde9MWXnrBoyptF93zLtc/+5lkTR0z3fXZ1noPvc/OFP3rHoxd/\ntqs7rUe8d90ff+onm+bq+2zyIbde8PU3P3TJlOfRY/5x7ZPOvqy1x3TPSbv89doj127o7u32\nuX+rw3c97wl/eptTu/f2+hNPvc/p56/da7qfOX/5uvzMWbL75b2Ow9of/ucx63/xucd0b9N9\nAgSGW2DBcHdf7wkQIECAAAECBAgQIECAQH8CCuD+nKxFgAABAgQIECBAgAABAkMuoAAe8gOo\n+wQIECBAgAABAgQIECDQn4ACuD8naxEgQIAAAQIECBAgQIDAkAsogIf8AOo+AQIECBAgQIAA\nAQIECPQnoADuz8laBAgQIECAAAECBAgQIDDkAgrgIT+Auk+AAAECBAgQIECAAAEC/QkogPtz\nshYBAgQIECBAgAABAgQIDLnAoiHv/9Z0f488aLdkaXJ1cmVyTaIRIECAAAECBAgQIECAwAgL\njMsV4FvnGL43uSS5PDk7OT05P6ki+LfJu5J9Eo0AAQIECBAgQIAAAQIERlBgHK4AvzzH7ZXt\nY/e73J6WVBFchW9dCd4zOSR5WvLQ5NnJhxONAAECBAgQIECAAAECBEZIYNQL4IfnWFXx+4Xk\npckPk15tIjPvmrwxOSk5Jzk10QgQIECAAAECBAgQIEBgRASq8BvlVsXsHZObJ9f2MdD6/eBz\nk7oC/Iw+1p9ulbqq/NpkyXQrdM2vj17fN6nfS17XtWwu79Z+v5EsnmYne2X+xqR+T7q71cfn\nb5DUx8h7tTKYTK7osbDOuwOTC5Jap7vVcah16kp9dyujg2+4z6LVSxYt2NC98KxL1q1Ymrd1\nDtxzyaruZes3blp41iUbdmktXHxVa2LR2u7lrQ1r9tplSWvi4D0mLu1etnHT5IJf/6G1d+bX\neKc+dvOnCeoNpcu6H9u+f1BuL0rKs7sdtNPi1tJD9p7a58nW5MSZF61fkQfUx/ev6n5g7u+a\nlMkfeiyrWeVcj11fd7pajv/E8taiZb37vGHNPrFaHatruh7Xam24NvvdtDDz6/ulV6tzoxx7\nnc/7L17Y2uXwfaeOtzZ0xkXrarx13vQ6/rtk/vLk90mvdsPWgsVrWgsWrZ6ycOO6XVqTG8vq\nnCnLMmPBROuG++3aWrvbsokp47306sldLrumtSwna/36RK+2f2auTNb0WLhT5tWnTS7usaxm\n1WPr2E7tc45v+rXPjfed6Hl8z7xkcu9Nk9d9f/ayqrHW9/CFSa+2b2bWPuvTMN2tjPdrLdqp\n534Xblyzz+47tzbss3xiyvf3yrWTyy5a2apjWL9a0qvV8059D035Hs28ei6q5T37HItD9tip\nNbnPiomyvl675trJpeddeZ1z7bfX80p9/9b3wZTHZt6y5KD2eKc+dsOaej6R8bdFAAAdSUlE\nQVSrY9vrvKvvgwOS6Z4Lt+V59MDWxIJFrYVLpzi3Nm1c2Nq0rrZ9TjLluTDzZnoereeqw1oL\nl13empiY+tgNa3cPYT1X1XN0r1bPKxclm3oszGNbZdLreaV+bhzeWrjkitbEwqnPSZv3W9uc\nznKm59F6LqyfuVOevzOv2o0O3bO1cqfFE1NeC1xw5eRuqzbPPW/zqlO+3ijPhSvzXDjlse3n\nwhpXfcKsVzvi4D1aq3ZZMjHl58ZFKyd3v2pta/HkNN9nE3kOvsHurTUrlk5M+R79/VWTK65c\n01qUk7Xnc/DEROvwA3Zrrd516cSU55VLrppcfsWa1pI89pxeHc732eF5Llyd58Ipjy2rNetb\nS260T+/npDN+P7l3tlvHvtf32e4LF7T2OnK6x+b5bHLyuuf+qed7qzXj8+jCidYRey1fsHGP\n5VOf+y++cv0uq9ZOLjxy/yW9foa2fn3xuhWbWnk90ev7bOP6POPkdUOrdVYvq8yb6Xm0zsd6\n3un5fNZ+bD2vDPxcmMds9fNo+7F1LvfyqOeG/ZLpvvdneh7t57mwnm96nRv9PLaek+bT69F0\nJz83Nh/fXs+FMz0H12O39nm0HlvPn3dPev6MrhW0mQXqRB/ldnQGd1oy9YdW71HXk+5Pkzop\nt2erJ4PvJL2Khe3Zj2HYVxmtPfsPG6qY6PWEs379xtZEiqheBUGN78DWxvV5gbS+12MXXLOu\ntfD030/2+qFQj60fglNftNWSbWur8oJibfo83Qu3+j7tVVht216vK0LyUmXDmunGuzxWeSGz\nvtd5WX47b2UHrs4x2pTxVmHeq9UPwilFaK8Ve8xb29q0/spkyovNrFs/eKsw69lSSK5J4bYy\nL0p7Wddx363nA+d25rr0a/UM52S9KOz3+W2QntYxXzPduZFXIcvyhsCay66Z7PXCrfyqkJ31\nVsfostWtay9b3fN7tL5P6gVnTuqBWx3fGm+vF2a1sRpPnT/bu61pTWbUvb9H603Cek6qF4WD\ntnrM2tbGtfVistdzYX0P1vZnu9W+st91td9e/a59ztXrkjXnXl7F1eR0x3HpDINdk+fC9Hl9\nr+f/Ot/qDZTp2przrqgX7ZPTP4/2Pr51Ii+/4Moq6Hs+tvzq+PdsKSTXXHhl64oLW5O9nh/q\nsct7PjAz28+FV+a5cLrn0V1neE6qnwu9xlq7u3bjptY1W3hsr33WY2dsGydb11yyatNVl6xa\nN6VozwPr+Owxw8+cnHebrs73Wa+fO+VX3w8aAQIEhkbgi+npr5J+X4zVuzVVDLw+0QgQIECA\nAAECBAgQIECAwNAIPDY9rXdnP53cYYZe17vOd03qKmy9O3yXRCNAgAABAgQIECBAgAABAkMj\nUIXtc5P6WEsVwucn/5t8NvlI+7Y+Il2/n1HL6+NNz0k0AgQIECBAgAABAgQIECAwlAKHp9dV\n8NYv9Veh25kqjn+dvCE5ONEIECBAgAABAgQIECBAYAQF6grpuLX6S5H1x2zqjyLUH+GZ7o+e\nZJFGgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgMD8EhjH\nj0DPryOw43tT/9/O/7jb8cdBDwgQIECAAAECBAhsSaD+l3dF20oBBfBWwo3Iw26XcXw3cR6M\nyAE1DAIECBAgQIAAgZEWqD/me2zy/ZEe5RwObtEcbtum57/AunSxit8TklXzv7t6OEQCX01f\nX5rUvxnTCMyWwFuyoZ8n75mtDdoOgQg8Nbll4t8gOh1mU+BO2dhrkuNnc6O2NfYCKyJwclKv\n4bWtFFAAbyXciD3sexnPFSM2JsPZsQKbsvvTEwXwjj0Oo7b3qzKg+nd2zqtRO7I7djz3ze4P\ncV7t2IMwgnvfI2Oqn4Wer0bw4O7AIdV5pW2jwIJtfLyHEyBAgAABAgQIECBAgACBoRBQAA/F\nYdJJAgQIECBAgAABAgQIENhWAQXwtgp6PAECBAgQIECAAAECBAgMhYACeCgOk04SIECAAAEC\nBAgQIECAwLYKKIC3VdDjCRAgQIAAAQIECBAgQGAoBBTAQ3GYdJIAAQIECBAgQIAAAQIEtlVA\nAbytgh5PgAABAgQIECBAgAABAkMhoAAeisOkkwQIECBAgAABAgQIECCwrQIK4G0V9HgCBAgQ\nIECAAAECBAgQGAoBBfBQHKY56+S6bHky2TBne7DhcRWoc2v9uA7euOdMoM6rikZgNgXqucp5\nNZuitlUCzivnwVwI1Gv2eu3uOWsudG1zbARuNDYjNdDtKXB4duYNtu0pPh772j/DXD4eQzXK\n7ShQ51SdWxqB2RSon4H1s1AjMNsCXrvPtqjtESBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQI\nECBAgAABAtsqsHBbN+DxQytwUHp+96RuL0nWJ9r4CRyWId8v+dkMQx/kXKnnlDslxyYbksuT\n6dpcrTvd/syfe4Gds4vbJHdJdk+uSq5NerW5Ov6DbLf6Ncj53Wsc5s29wIrsop5Xbp2sTK5O\npmtzefwHOVcGWXe6sZi/fQWOz+4OSM6bZreDHNO5WnfQ83uaoZg9hwKHZNv1869Xrsn8TV37\nng/nivOq66C4O5oCr8ywquCdbGdDbl+YaOMlsGuG+8tk1QzDHuRcOTLb+VXSnFd1+4vk4KS7\nzdW63ftxf/sJPCG7+n3SefyrAH52jy7M1fEfZLvVrUHO7x7DMGs7CDw6+/hD0nlenZr7+/bY\n91we/0HOlUHW7TEMs3aAwH2zzzrHTp5m34Mc07lad9Dze5qhmD2HAvW81Plc1T194659z4dz\nxXnVdVDcHU2Be2VY9Q358aTeTT82+UJS856VaOMhsEeG2Rz36QrgQc6ViWzvlKQKnsclN0qe\nmqxOzk12SZo2V+s223e7/QXqXKl3tc9OXpzcMqnC9/SknlsenzRtro7/INutvgxyfjd9d7t9\nBe6W3dUbtL9O6vmkzqu/T9YkNW9p0rS5PP6DnCuDrNv03e2OFdgnu784qeeqXgXwIMd0rtYd\n9PzesaLju/d7t8+jL+X2zT1S51rT5sO54rxqjobbkRaojyfWC9Tzk/q4Q9OWZKLm18d+Ouc3\ny92OlsCDM5wLk/phf23SqwAe9Fz5i/b2np7bzvbU3Kn9dM6fq3U792t6+wp8Lbur41w//Dvb\n7XOn5tcnAZo2V8d/kO0Oen43fXe7fQX+J7ur86d+TaOzvT93an69gGzaXB3/Qc6VQdZt+u12\nxwt8Kl24JKlzqrsAHuSYztW6JTTI+V3raztG4EXZbZ1Hd9/C7ufLueK82sKBsng0BO6TYdQ3\n5mt7DOc17WXdLzR6rGrWEAs058ClGcMDkx8mvQrgZr1+z5XvZDtrk/qdl862a+7U1Zrvdcyc\nq3U7dmFyOwosyL6+m1SR2+sNtLoKXFfxmmVzdfwH2e590h/PhUGY563eQHtdUlcpOlt9oqCO\nX33KoGlzdfwHOVcGWbfpt9sdK/C07L7OpQe1b+uTUZ1tkGM6V+tWf76T9PsztrP/prevwEey\nu/o0VP3dgpnafDlXxva8qhcu2vgI1Medq9WL1e7WzLtd9wL3R0qgCpFXJzdOPj3DyAY5VxZn\nO8ckZyZXdm2zPhJdBdCtklpvrtbNprUdJFA/7Ot8uUWysasPy3L/gOScpJbN1fEfZLvpxnX9\nrdvmea+mm9bM81zYiOy42/dk180VlaYXVQzXp1iqfWXzzUDnVT1kkOe3uVq33XU3O1DgyOz7\nTcnbk+7Ct+nWXB3/QbY76PNb03e321+geS20JLt+dPLc5IRkp6SzDXL8B1l3kHNlkHU7+z4S\n04tGYhQG0a/Afu0VL+vxgMvb8w7sscys0RGo30upbKkNcq7skY3Vk32v86r2U+dWPdHuk1QB\nPhfrXpjtavNPoIqXXZN3trs2X86VQc7v+ac6nj26eYb9qOT+Sb2h9jdJfeqg2iDnVT1XDHL8\n52rd6zruyw4TqNe/JyX1K2EvnKEXc3X8B9nuoOf3DMOxaA4Fds62b5z8ITk76bwK/Ovcf1zS\nvME6yPEfZN1BzpVBXo+N3GssBXDOxjFq9UK0Wn38tbs1BfAu3QvcH0uBQc6VmdYtvM5zqz5q\nVq3XOVjzt3bdeqw2vwQeke68PKkf/K9Iqs2Xc2WmfnSeg5t77et8EPjrdOKp7Y78Jredv6s5\n0/Gsh3Qf05nW317rtofiZgcJ/H32e+vkzsnqpD6t0qvNh3Nlpj5Un7vP2V7jMG/uBY7OLuqT\ntVWE/l1Sf8OgPrFShW+9yfKZ5GZJHa+Zjmn38ZytdbPb650rg7weq8eOVPMR6JE6nFsczNr2\nGr2Oe/P7ed0fYdziRq0wkgKDnCszrVs4nefWXK07kgdhiAf1xPT9Q0m9E/6nyZqk2lwd/0G2\nu6V+dJ6v13Xal3kh8Kr0Yv+k/qBeHe8fJk9Lqs3l8Z9p293nyiDrbu65rztCoIreFyevTr63\nhQ4Mckx3xLrV/e7zcAtDsniOBM7Kdutjz8cnr09+lfwyeUnyxmTf5HlJtflwrszUh+rjSJ9X\nvQqhGrQ2mgLNRxj27DG8Zt7KHsvMGj+BQc6Vi8NT7yQ251C3VjO/zq25Wrd7n+7vOIG66vv+\n5Pzkbkm9CGjaXB3/QbZbfRnk/G767nbHCtT59Pvk3cmjkkXJs5Jqc3n8BzlXBll3c8993d4C\n9bHUDyU/Terf1NTHVptk8roX/XV/Sd1JG+SYztW6g57fm3vu6/YWuCQ7/M/k2z12/MH2vPrU\nQbX5cK6M9XmlAN58Io7L136+4S4YFwzjnFFgkHOlfo+knvibQrd7wzW/PmJWfyBrrtbt3qf7\n21+gPur1luSVSV1VuVNyZtLZ5ur4D7Ld6s8g53dn/03PD4H63d/666W3TA5J5vL4D3KuDLJu\nuq3tAIEqQG6Y1O3K5Jp2LstttT9Oat4H6k7aIMd0rtYd9Pze3HNf55NAfRqqWvNx5vlwroz1\neaUA3nxCjsvX5krM3XsMuJn33R7LzBo/gUHPlVr/5sneXVT75H79zssPkubj9XO1bteu3d2O\nAvWz5H3Js5NPJscldbWuV5ur4z/odqtvzfNeZz+beZ4LO1W2//Ty7PI3yVen2fWm9vyr27dz\ndfxru9Wa82Lzvc1fm3nNuTLIup3bMb39BKrweGuPvKPdhd+1lzW/Yz7IMZ2rdatrte1+f8bW\n+tr2F3hudnlGUh+D7m43bc+o5dXmy7nivNp8PHwdA4H62M9FSfMuVA15t6Q+CvGjpD5Wpo2P\nQP0eXa//A1wCg5wrD8n6k0n9oYfO9re5U/Mf1jFzrtbt2IXJ7SzwF9lfHeePJ83vDU3Xhbk6\n/oNst/r208Rz4XRHaX7Mb944q6t1ne1OuVNvqNXPrKbN5fEf5FwZZN2m7253vMCydKGew77Q\noyuDHNO5Wvch7f718zO2xxDM2g4CD20fo5/ntj4R1bSarvOqzq+7NTNzOx/OFedVxwExOdoC\n9c5UfRPWC4sqSh6eVBFUH4W4TaKNl8BMBfAg50pdAfxlUi9K/yGpj5G9un2/iqLONlfrdu7D\n9PYT2Cu7uiKp55WvJHUFuFfqil61uTr+g2y3+jHI+V3ra9tf4I+yy/XJJcnrknsmf5PUR1ev\nTToL47k8/oOcK4OsmyFo80RgpgJ4kGM6V+sOen7PE9ax6ka9+VufWKmfhV9LHp88OPliUvPe\nk3S2+XCuOK86j4jpkRd4bEZ4eVLfkJWafnKijZ/ATAVwaQxyruyd9T+f1EcTm3Pr5Ezvn3S3\nuVq3ez/uz73An2YXzfGe6XaPjq7M1fEfZLvVnUHO747um9yOAvVm2ulJ57l1Wu7fqkcf5vL4\nD3KuDLJuj2GYtQMEZiqAqzuDHNO5WnfQ83sHMI79Luvn3DuSuqjUPGfVv32sN+56tflwrjiv\neh0Z80ZWoD6ScaPkFsnSkR2lgc2GwKDnyors9LZJr8K3uz9ztW73ftyfnwJzdfwH2e6g5/f8\nlBz9Xh2YId4+2b2Poc7V8R/kXBlk3T6GZJV5IDDIMZ2rdYthkPN7HrCNZRfqDZWjksP6GP18\nOVecV30cLKsQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQINBDYGGPeWYRIECAAIFxE1icAT8/OTj5xbgNvs/xMuoTymoE\nCBAgQIAAAQIECBCYzwKPTecmkyfP507u4L4x2sEHwO4JECBAYNsFFmz7JmyBAAECBAgQIECA\nAAECBAjMfwEfgZ7/x0gPCRAgQGBuBe6azd8/uV1yabJHcnZybVJtUfKA5FHJCcleyVnJhqRp\n9ZhHJquTupL8oOQJyX7JRUnNX5bcN6mrzLWvC5MrkqYdl4k7JPUR7HsmT0yOSS5LLk96tX76\nVv19RHJNckjyrGTP5NxkfVLtLskDk8ckxyYHJL9NmjHOZPTHWa+W/zypsTdtSSYel9S+zkmq\nHZ/cJqltPzUpzzK4JKnWz3g2r+krAQIECBAgQIAAAQIECAwscFIeUYVbk02Zvkl7K4fn9jvt\nZStzWwVyrffL5OikaTVd81+d/KY9XcVlzTszOTD5Wvv+uvZtFaS3Tpr28UzU9t+c1OPOSKo4\nrOl3Jd2t377dNg+sbbwmubI9Xfer6N0t+Wh7Xo37D+3pZv83yP1qMxl9Ictr/Z1qxY5WbwrU\n/E90zPtMpqvwfltSyypfSqr1O57Na/tKgAABAgQIECBAgAABAlsl8Ng8qoqxujrbtIlMfC/Z\nmNSVzLpf7V5JXZWtArWuclZrCuAqIj+UVOFYV38/mNR2q9j9XHLnpB7zgqTm/1fStCqAa15t\n+4/aM+uK6LuTmv+09ry6GaRvTQG8Po/7WFJXoZ+fVHtFUtv+l2TvpNrNkv+X1PwqmpvWy6iW\nDVoAb8hjqrB/SvLo5G7JIOPJ6hoBAgQIECBAgAABAgQIbK1Ar+KuPvJcRWBdtexur8qMWvb0\n9oKmAD4v95e259XN7ZJab1Wya9K0KvjWJT9pZuS2KYCf3TGvJmt75ycX1J12G6RvTQFc2+js\nW22qCt8vJjvXnY7WPKYK5qb1MqplgxbA5fFXzUbbt4OMp+uh7hIgQIAAgf4FFvW/qjUJECBA\ngMBYCdyxPdqv5rYK3M5WH4GuVgVu58eT6/d3r60F7faz9m1dLb6qmZnbKgJ/n6zomNdMfriZ\naN/W9qpI/fNk36R+X3Zr+lbFdmffcrf11/Wlo9VV4Jsmx7fndRfGHatu0+R3uh69NePp2oS7\nBAgQIEBgywIK4C0bWYMAAQIExlPgyPaw3zTD8G/Utezcrvv18elq9bu33a1Z1jm/Pipdvwfc\n3erqbbWjkq8kW9O3s2sDXW1B7j8+eWJS294rqVYfUa5WV6rnonX3ZWvGMxf9sk0CBAgQGHEB\nBfCIH2DDI0CAAIGtFljbfmR99Leu1vZqnVd1a3l9rHlb2uI8uIrOukLc2XZt37m4fTtbfXtb\ntvcXyVnJR5P6nee6UnxhclEySOsulntd3W621+20NeNptuWWAAECBAj0LaAA7pvKigQIECAw\nZgJntsdbRW5dde1su+dOffy5KUg7l23LdP2BrEOTc7o2Uh9LXp2c3p4/G32rj1NX8Vsf566x\nrEmadpf2xMJmxgy3TfG6LOtUH5t2RDPRx+1sjKeP3ViFAAECBMZdoD76pBEgQIAAgXEXWN8G\n2KUD4tOZriuxL0m6C8G6cvql5E7JbLfu38u9VXZw7+SbSfOx6dno2w3bHa+r253Fb13JrcK4\nWl2Rblovo1rWfGS7+b3hZv0ntie6rww3yztvZ2M8ndszTYAAAQIECBAgQIAAAQLTCByX+VXs\n1pXI1yUHJ9Xel9T8byWPTB6cfCCpeZ9KmlZ/JKvmvbWZ0b6tT1rV/C93za+75yT10eOmfTwT\nte6m5O1JFb1ViP4hOS85IOls/fat+YvO3b/LXH/gqv6gVu3z1UkV8zXG+r+99bvIVRTXx6Gb\ndlwmat1uoxPa86uQfmnyxOSTSX2Euq6e13TTPpOJ2kbzke5mft32O57Ox5gmQIAAAQIECBAg\nQIAAgQEFqlD9z6SuclaB9rCkWn1S6m+SK5OaX6kCtf490P5J02azAH5sNlofra591V9t/lJS\n2+9u/fZtugK4tlf/b/jXSTO2+h+9VaQe1r6tK843SKpNZ1TLnpVUsdv4/DDTRyS/S6qgbtpM\nBXC/42m25ZYAAQIECBAgQIAAAQIEtkFgpzy2fje2VzskM+vjyL2uXvZaf9B5H88DqoDcK6mP\nDd8kmekPSWXx/7Vt6VsVnoclVWTX7/FuqU1nVNu5WbL3ljbQx/JtGU8fm7cKAQIECBAgQIAA\nAQIECOxIgc4CeEf2w74JECBAgMDICtS7tRoBAgQIECBAgAABAgQIEBh5AQXwyB9iAyRAgACB\nIRGo3z9el9THoDUCBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAIHZE/j/AOYyielx9neDAAAA\nAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r <- runif(n=n,min=0,max=1)\n",
    "sample <- rep(NA,n)\n",
    "sample[r<0.5] <- 3000 + (4000-3000)*(r[r<0.5]/0.5)\n",
    "sample[r>=0.5] <- 4000 + (40000-4000)*((r[r>=0.5]-0.5)/0.5)\n",
    "\n",
    "xlab <- 'temperature'\n",
    "ylab <- 'freq'\n",
    "\n",
    "bins <- seq(0, 50000, 500)\n",
    "\n",
    "# make new colours with transparency\n",
    "or <- alpha('orange', 0.4)\n",
    "bl <- alpha(cbPal[6], 0.4)\n",
    "\n",
    "hist(observed, breaks=bins, xlab=xlab, ylab=ylab, col=bl, main='')\n",
    "hist(sample, breaks=bins, xlab=xlab, ylab=ylab, col=or, add=TRUE)\n",
    "legend('topright', legend=c('sample from theoretical pdf','observed data'), \n",
    "       fill=c(or,bl), cex=0.8, y.intersp=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How can we test more formally whether the observed data appear to be drawn from the theoretical distribution?\n",
    "\n",
    "Here we have a theoretical distribution *which is not directly related to any of the standard statistical distributions*, so parametric methods such as the Shapiro-Wilk test are not applicable.\n",
    "\n",
    "However, we can still perform a *non-parametric* goodness-of-fit test, by comparing the theoretical *cumulative* distributionfunction (cdf) with the empirical one. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "althea_cdf_single <- function(x){\n",
    "    if(x<3000) return(0)\n",
    "    else if(x<4000) return(0.5*(x-3000)/(4000-3000))\n",
    "    else if(x<40000) return(0.5 + 0.5*(x-4000)/(40000-4000))\n",
    "    else return(1)\n",
    "}\n",
    "\n",
    "# We can use the Vectorize() function to make a vector-friendly version of this cdf:\n",
    "althea_cdf <- Vectorize(althea_cdf_single)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The empirical cdf is derived from the observed data using the `ecdf()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAHgCAYAAABq5QSEAAAEGWlDQ1BrQ0dDb2xvclNwYWNl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\nQAABBBBAAAEEqifw//UqWT34Ah6OAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "empirical_cdf <- ecdf(observed)\n",
    "\n",
    "x <- seq(0,50000)\n",
    "\n",
    "xlab <- 'temperature'\n",
    "ylab <- 'cumulative probability'\n",
    "    \n",
    "plot(x, althea_cdf(x), type='l', col='orange', xlab=xlab, ylab=ylab)\n",
    "lines(x, empirical_cdf(x), type='l', col=cbPal[6])\n",
    "legend('bottomright', legend=c('theoretical cdf','empirical cdf'), \n",
    "       col=c('orange',cbPal[6]), lty=c(1,1), cex=0.8, y.intersp=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kolmogorov-Smirnov test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Theory\n",
    "\n",
    "The [*Kolmogorov-Smirnov test*](https://en.wikipedia.org/wiki/Kolmogorov–Smirnov_test) (or K-S test) examines the deviation of the empirical cdf, $F_n(x)$, from the theoretical one, $F(x)$, to assess the goodness-of-fit. The test statistic is the quantity\n",
    "\n",
    "$$\n",
    "D_n= \\sup_x |F_n(x)-F(x)|,\n",
    "$$\n",
    "\n",
    "i.e. the greatest vertical distance between the two lines in the plot above.\n",
    "\n",
    "The distribution of $D_n$ under the null hypothesis $H_0: F_n(x) = F(x)$ is called the *Kolmogorov distribution*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Application\n",
    "\n",
    "In our example,\n",
    "\n",
    "$H_0$: $F_n(x) = F(x)$  : The observed temperature distribution of hypergiants is described by Althea's theory.\n",
    "\n",
    "$H_1$: $F_n(x) \\ne F(x)$  : The observed temperature distribution of hypergiants is not described by Althea's theory.\n",
    "\n",
    "$\\alpha = 0.05$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Graphically, we can plot $D_n$ for each $x$-value in the plot above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"D_n: 0.1995\"\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAHgCAYAAABq5QSEAAAEGWlDQ1BrQ0dDb2xvclNwYWNl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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xlab <- 'temperature'\n",
    "ylab <- 'empirical cdf - theoretical cdf'\n",
    "\n",
    "x <- seq(0,50000,1)\n",
    "y_values <- empirical_cdf(x) - althea_cdf(x)\n",
    "\n",
    "plot(x, y_values, type='l', xlab=xlab, ylab=ylab, col='black')\n",
    "\n",
    "D_n <- max(abs(y_values))\n",
    "print(paste('D_n:', D_n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test itself is easy in R:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in ks.test(observed, althea_cdf):\n",
      "“ties should not be present for the Kolmogorov-Smirnov test”"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\tOne-sample Kolmogorov-Smirnov test\n",
      "\n",
      "data:  observed\n",
      "D = 0.2, p-value = 0.08152\n",
      "alternative hypothesis: two-sided\n",
      "\n"
     ]
    }
   ],
   "source": [
    "result <- ks.test(observed, althea_cdf)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Owing to the rounding in the observed data, there are stars with identical temperatures, i.e. 'ties'. A warning appears because this can affect the calculation of the test statistic. Looking at the cdf plots, it appears unlikely that ties are responsible for much of the deviation between the two lines, so our results should still be reliable.\n",
    "\n",
    "The resulting $p > \\alpha$, so we accept the null hypothesis: the observed data appear to be compatible with Althea's theory."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other applications of the K-S test\n",
    "\n",
    "#### Goodness of fit\n",
    "\n",
    "The K-S test can be used as an alternative method for testing normality, or as a goodness-of-fit test for any other theoretical distribution. However, the standard test is only valid if the parameters (e.g. mean and variance) are *not* estimated from the data. \n",
    "\n",
    "If parameters *are* estimated from the data, we will need to use simulation to find an empirical distribution for $D_n$ under $H_0$.\n",
    "\n",
    "\n",
    "#### Two sample test\n",
    "\n",
    "`ks.test()` can also be used to compare two samples (in the absence of a theoretical cdf) to test whether they follow the same distribution. \n",
    "\n",
    "---\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
